Heinz Han{\ss}mann
Quasi-periodic Motions of a Rigid Body I  ---   
Quadratic Hamiltonians on the Sphere with a Distinguished Parameter
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ABSTRACT.  The motion of a dynamically symmetric rigid body, fixed at 
one point and subject to an affine (constant$+$linear) force field is 
studied. The force being weak, the system is treated as a perturbation 
of the Euler top, a superintegrable system. Averaging along the invariant 
$2$-tori of the Euler top yields a normal form which can be reduced to 
one degree of freedom, parametrised by the corresponding actions. The 
behaviour of this family is used to identify quasi-periodic motions of 
the rigid body with two or three independent frequencies.